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For a bivariate data, x¯=53, y¯=28, byx = −1.5 and bxy = −0.2. Estimate y when x = 50. - Mathematics and Statistics

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प्रश्न

For a bivariate data, `bar x = 53`, `bar y = 28`, byx = −1.5 and bxy = −0.2. Estimate y when x = 50.

बेरीज
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उत्तर

Given:

`bar x = 53`,

`bar y = 28`,

byx = −1.5 and

bxy = −0.2

Regression equation of y on x is,

y = a + byx . x

byx = −1.5

`a = bar y − b_(yx) . bar x`

= 28 −( −1.5)53

= 28 + 79.5

= 107.5

∴ y = 107.5 − 1.5 x

i.e. y = −1.5 x + 107.5

Put x = 50

∴ y = −1.5(50) + 107.5

∴ y = −75 + 107.5

∴ y = 32.5

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Properties of Regression Coefficients
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पाठ 3: Linear Regression - Exercise 3.3 [पृष्ठ ५०]

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